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Pasquale Commendatore and Ingrid Kubin

Dynamic effects of regulation and deregulation in goods and labour markets

Working Paper

Original Citation:Commendatore, Pasquale and Kubin, Ingrid (2005) Dynamic effects of regulation and deregulationin goods and labour markets. Working Papers Series "Growth and Employment in Europe:Sustainability and Competitiveness", 49. Inst. für Volkswirtschaftstheorie und -politik, WU ViennaUniversity of Economics and Business, Vienna.

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Wirtschaftsuniversität Wien Vienna University of Economics and Business Administration

Working Papers Series:

Growth and Employment in Europe: Sustainability and Competitiveness

Working Paper No. 49

DYNAMIC EFFECTS OF REGULATION AND DEREGULATION IN GOODS AND LABOUR MARKETS

Pasquale Commendatore and Ingrid Kubin

May, 2005

This working paper series presents research results of the WU-Research Focus:

Growth and Employment in Europe, Sustainability and Competitiveness The papers are available online under: http://www.wu-wien.ac.at/inst/vw1/gee/workp.html

DYNAMIC EFFECTS OF REGULATION AND DEREGULATION IN GOODS AND

LABOUR MARKETS

by

Pasquale Commendatore Università di Napoli 'Federico II' , Dipartimento di Teoria Economica e Applicazioni

Via Rodinò 22 80138, Napoli, Italy

Tel.: +39 081 253 7447 email: commenda@unina.it

and

Ingrid Kubin (corresponding author)

Vienna University of Economics and Business Administration (WU) Augasse 2-6

A-1090, Vienna, Austria Tel.: +43 31336 4456

email: ingrid.kubin@wu-wien.ac.at

Abstract

Modern macroeconomic models with a Keynesian flavour usually involve nominal rigidities in wages and goods prices. A typical model is static and combines wage bargaining in the labour markets and monopolistic competition in the goods markets. As central policy implication it follows that deregulating labour and/or goods markets increases equilibrium employment. We reassess the consequences of deregulation in a dynamic model. It still increases employment at the fixed point, which corresponds to the static equilibrium solution. However, deregulation may also lead to stability loss and endogenous fluctuations. Acknowledgements An earlier version of the paper was presented at Workshops in Naples, Aix, Vienna, Salerno and Helsinki. We would like to thank Ulrich Berger, Peter Flaschel, Leo Kaas, Elisabetta Michetti, Carlo Panico, Florian Wagener and participants of the Workshops for helpful comments. The usual caveat applies. Keywords Labour and goods markets deregulation, monopolistic competition, business cycles JEL E1

1

Dynamic effects of regulation and deregulation in goods

and labour markets

Pasquale Commendatore, Università di Napoli ‘Federico II’

Ingrid Kubin, Vienna University of Economics and Business Administration

1. Introduction

Recently, Blanchard and Giavazzi (2003) analysed the macroeconomic effects of regulation

and deregulation in goods and labour markets. Their framework combines monopolistic

competition in the goods market with wage bargaining in the labour market. In the short

run, deregulation primarily changes the distribution of rents; in the long run this induces via

firms entry and exit changes in employment levels.

Their model belongs to the long tradition of macroeconomic models with a Keynesian

flavour, which use Dixit-Stiglitz monopolistic competition as a microfoundation for

nominal rigidities and price setting power in the goods market.1 Keynesian features studied

1 The widely used approach of specifying wage and price setting equations (see e.g. Nickel,

1990; Layard et al., 1991; or Blanchard, 2003; and for empirical applications various

2

in such models are the possibility of unemployment (e.g. Blanchard and Kiyotaki, 1987;

d’Aspremont et al., 1990), wage price spirals (Blanchard, 1986) and multiple equilibria

(e.g. d’Aspremont et al., 1995; Linnemann, 2001) and that fiscal policy has income

multiplier effects (Heijdra and Ligthart, 1997; Heijdra et al., 1998; see also Solow, 1998).

Typically, all these models focus on what Blanchard and Giavazzi (2003) call short run

general equilibrium – i.e. a position with a fixed number of firms in which all firms choose

the same price and quantity and in which goods markets clear – and on the long run general

equilibrium – a position with zero profits due to firm entry and exit. How those equilibria

are brought about is usually not modelled explicitly, with Maussner (1992, 1996) and, more

recently, Jin (2001) and Currie and Kubin (2002) as the only exceptions known to us.

In particular, the transition to the short run equilibrium is not simple and obvious because

even in equilibrium firms do not act upon a basis of knowing fully the model. Firms do not

take into account that their decisions influence aggregate variables or that other firms may

react. In this sense, their equilibrium pricing decisions are based on a price elasticity that is

partial (i.e. it takes the aggregate income, the other prices and the price index as given) and

that is higher than the one holding in the aggregate (which allows for all

interdependencies). Given these limitations to knowledge in equilibrium, it would be

inconsistent to assume full knowledge of the model out-of-equilibrium. This raises the

question how the equilibrium is brought about, esp. how the equilibrium quantities are

found.

analyses by the European Commission, e.g. McMorrow and Roeger, 2000; Bains et al.,

2002) can also be seen in this tradition.

3

We suppose rational behaviour in the sense that agents hold outside equilibrium the same

information as in a short run (or in a long run) equilibrium and act consistently. Following

Maussner (1992, 1996) and Currie and Kubin (2002), we assume that firms know that the

demand functions they face are iso-elastic and that they know the value of the partial price

elasticity but that they do not know all the interdependencies of the aggregate model. In

particular, they do not know the position of the demand functions which they anticipate on

the basis of market positions realized in the past. 2

We develop a model which closely follows Blanchard and Giavazzi’s (2003) set up but

which is amended by a dynamic process focusing on the transition to the short run general

equilibrium (and by a more explicit specification of the reservation wage). The short run

general equilibrium solution is a fixed point of our dynamic model. However – and this is

the main point – depending upon the parameters the fixed point may lose stability through a

Flip-bifurcation giving rise to cyclical solutions and endogenous fluctuations.3 We show

analytically that deregulation in goods and labour markets may lead to instability.

The paper is organized as follows: In the second section, we present our model:

monopolistically competitive firms bargain with unions over employment and wage rates

on the basis of firms’ anticipated demand functions and workers’ reservation wages. In the

third section, we explicitly add two dynamic components. First, the adjustment of the

2 Jin (2001) does not confine his analysis to the Dixit-Stiglitz variant of monopolistic

competition. In his framework, the demand functions need not be iso-elastic and firms base

their decisions on linear expected demand functions.

3 D’Aspremont et al. (1995) analyze endogenous fluctuations in what they call a Cournotian

monopolistic competition model. In contrast to our approach, the dynamics in their model

is equilibrium dynamics, which is driven by an overlapping generations structure and

variable mark-ups.

4

anticipated demand function on the basis of realized market prices and quantities; second,

the adjustment of the reservation wage on the basis of realized employment and wage rates.

We show that the first process in isolation leads to diverging time paths: deregulation leads

to instability. In the fourth and the fifth sections, we study two different specifications for

the reservation wage adjustment, each of which mirrors a different institutional set up. We

show that this second process may dampen the sharp instability result: deregulation may

still destabilize the economy; however, time paths do not diverge but fluctuate following a

period-two cycle or more complex trajectories. Some simulations complete the dynamic

explorations. The last section is left for concluding remarks.

2. The economic framework

The analysis, being framed in a dynamic setting, requires dealing explicitly with time. We

assume that during the time unit, which for expository purposes we call ‘Week t’, all events

occur according to a well-defined sequence. On Monday of Week t, firm i and the

associated union bargain over employment and the nominal wage rate on the basis of firms’

anticipated demand and workers’ nominal reservation wage. Production occurs during the

Week from Tuesday to Friday. On Friday, commodities are delivered to the market. Market

equilibrium determines the realized price. Finally, on Saturday firms and unions update the

information relevant for decisions in the following period concerning the employment, the

nominal wage rate and the realized price.

2.1 Firms and Households

The economy comprises a fixed number m of firms, each firm producing one differentiated

good in a regime of monopolistic competition; and L households, which own the existing

5

firms, each household supplying one unit of labour. Each firm i faces a union composed of

i LM

m= members, with i = 1 … m.

All firms share the same production technology, which involves only one input, labour,

used in a fixed proportion.4 Assuming that during Week t firm i employs itN workers, the

production of good i is:

( )i i it t tx f N N= = (1)

Household j’s preferences (j = 1 … L) towards good i are represented by a CES utility

function:

( )1 1 1

1

σσ σ

σ σ− −−

=

� �= � �� �

�m

j it t

i

U m c (2)

where 1 < σ < ∞ is the – constant – elasticity of substitution between goods and itc is the

consumption level of good i for the period. Note that, because of the factor 1σ

−m included in

the utility function, this specification does not represent a preference for goods variety; σ is

a parameter related only to the market power of a single good supplier (see Blanchard and

Kiyotaki, 1987; and also the discussion in Benassy, 1996). In Blanchard and Giavazzi

(2003), it is the central parameter for studying the effects of goods market deregulation.

Household j’s demand for good i is given by

i

jj tt

t t

Y pd

mP P

σ−� �

= � �� �

4 Note that Maussner (1992, 1996) uses a more general production function with a variable

marginal product of labour.

6

where Yj is the household j’s nominal income (profit income, work and non-work income)5

and where

( )1

11

1

1 mi

t ti

P pm

σσ −−

=

� �= � �� �� (3)

is the price index. Summing through j, we obtain the demand for goods i during Week t

it

tt t

pYd

mP P

σ−� �

= � �� �

(4)

where Y is the overall nominal income of the economy. Taking the income and the price

index as given,6 the partial elasticity of demand with respect to the own price therefore

reduces to σ− .

If the price of each good is the same, it tp p= , the price index becomes t tP p= and the

demand for an individual good simplifies to

tt

Yd

mp= (5)

in which the elasticity of demand with respect to the price is equal to 1− .

5 Note that the demand decision can also be interpreted as a decision under a cash-in-

advance constraint, see below section 2.3.

6 We thus neglect the Price Index Effect and the Ford Effect (see Yang and Heijdra, 1993;

Dixit and Stiglitz, 1993; and d’Aspremont et al., 1990, 1996). Linnemeier (2001) showed

that both effects are at the root of a possible multiplicity of equilibria. We prefer to

demonstrate our results in the simplest possible framework with a unique equilibrium.

7

Moving on to the description of the events occurring during ‘Week t’, most of our

discussion will be devoted to the crucial ones, that is, the bargaining process and the

determination of the market equilibrium.

2.2 Bargaining

As Blanchard and Giavazzi (2003), we employ the efficient bargaining model (McDonald

and Solow, 1983; Layard et al., 1990): During the Monday of Week t the parties (firm i and

the associated union) bargain over employment itN and the nominal wage rate i

tW for the

current period as to maximize

1i i i

i it t t tt t

t t

W WR p WN N

P P

β β−� � � �− −� � � �� � � �

%% % (6)

where 0 < β < 1 represents the relative bargaining power of the unions. We assume a

utilitarian trade union; and we observe that the CES indirect utility is given by the nominal

income deflated by an expected price index tP%, that all profits are distributed to the owners’

households, and that workers not finding employment in the firm under consideration are

expected to receive an alternative income or reservation wage in nominal terms, tWR .7

Finally, itp% denotes the anticipated price for good i; i.e. the price at which the quantity

produced is expected to be sold in the market on Friday.

The determination of the anticipated price is crucial to our model specification. Central to

the Dixit-Stiglitz model of monopolistic competition is that – even in equilibrium – firms

do not allow for all the interdependencies. Particularly, in their price setting decision, they

7 Blanchard and Giavazzi (2003) specify the alternative income in real terms. Further down,

in section 4, we provide a full discussion of this issue.

8

do not take into account that their decisions influence aggregate variables or that other

firms could react. They set equilibrium prices on the basis of a constant price elasticity

equal to σ− . Given the fact that even in equilibrium firms do not act on the basis of

knowing fully the model, it would be inconsistent to assume this knowledge outside

equilibrium. Therefore, following Maussner (1992, 1996) and Currie and Kubin (2002), we

assume that out-of-equilibrium firms have the same knowledge as in equilibrium; i.e. they

know that their demand function is iso-elastic and consider the elasticity to be equal to σ− .

However, they do not take into account all interdependencies. Consequently, firms have to

rely on past observations of market prices and quantities to anticipate the position of their

demand function. Each firm knows that it sold in the previous period a quantity 1ˆ

−td at a

price 1ˆ −tp . If the firm assumes that it can sell the same quantity at the same price as in the

previous period and that sales will react to a price change according to the elasticity of σ− ,

it will anticipate its demand function for the current period to be given by:

( )

( ) ( )1 1

ˆ ˆ it t t

t i it t

d p Kd

p p

σ

σ σ− −= =%

% % (7)

where itK is the position of the anticipated demand function.8

Using equations (1) and (7), we obtain the anticipated price itp% as

1σ� �

= � �� �

%i

i tt i

t

Kp

N (8)

8 In the main body of the paper we present the model with naïve expectations, i.e. only

information of the last period is used to estimate the position of the demand function; in the

Appendix we study also a version with adaptive expectations which is more general and

more complex but does not change the basic dynamic mechanism at work.

9

Returning to the bargaining problem of equation (6), we assume that the anticipated price as

given in equation (8) is common knowledge to both bargaining parties. Observing that –

consonant with the monopolistic competition set-up – the parties assume the expected price

index tP% to be independent of their decisions, the bargaining results in:

1 1

11 1

σ β βσ σ− +� � � �= = +� � � �− −� � � �

it t tW WR WR (9)

1

it t tN K WR

σσσ

−� � �= � � �−� ��

(10)

² 1 it tMR p WR

σσ−= =% (11)

Note that equations (10) and (11) are not independent results, equation (11) can be obtained

from equation (10) by taking constraint (8) into account.

Note in addition the familiar result from the efficient bargaining problem, namely that a

position is chosen off the profit maximum. In equation (9), the marginal revenue is equated

to the nominal reservation wage and not to the marginal cost (corresponding to the nominal

wage rate). It follows that the price is set as a mark-up over the reservation wage,

11

1σ� �= +� �−� �

%it tp WR .

Following Blanchard and Giavazzi (2003), we interpret a decrease in the mark-up (i.e. an

increase in σ) as goods market deregulation. It reduces the size of firm i’s anticipated rent

per unit of output, ( ) 11σ

� �− = � �−� �%i

t t tp WR WR . Labour market deregulation is reflected in

Blanchard and Giavazzi (2003) by a decrease in the relative bargaining power of the union,

β, which reduces the workers’ share in the rent, 1

1β

σ� �� �−� �

tWR (see equation (9)). In

10

addition, our model, as developed in the following sections, allows for labour market

deregulation in the form of changing the unemployment insurance scheme. This form of

labour market deregulation may also impinge on the bargaining outcome (and on the size of

the rent) through its effects on the nominal reservation wage.

During Week t, at the end of contracting, firm i employs itN workers, pays the nominal

wage rate itW and anticipates the price i

tp%. Figure 1 depicts the bargaining equilibrium.

Given the reservation wage tWR and the position of the anticipated demand function Kt, the

bargain determines the employment level itN and the wage rate i

tW in firm i. Each firm

expects to sell its output at an anticipated price itp%.9

2.3 Temporary goods markets equilibrium

The characteristics of the goods market equilibrium follow from the symmetry assumption,

that is, all firms behave identically. Each firm pays the same wage it tW W= , hires the same

number of workers, it tN N= , and produces and supplies the same quantity i

t tx x= . They

envisage to sell these quantities at an identical anticipated price it tp p=% %. At the end of the

production period, on Friday, each firm supplies xt to the (identical) true demand function dt

(see equation (5)). In contrast to the anticipated demand function, the true demand function

takes into account the reactions of all other firms; and, therefore, it has an elasticity of 1−

9 With efficient bargaining the employment level and thus the output is determined in the

bargaining process. In contrast, Maussner (1992, 1996) assumes that output levels are

adjusted to the demand coming forward at the set prices. This is compatible with constant

wages and with monopoly trade unions (the cases he analyses) but not with efficient

bargaining. See also Jin (2001).

11

(instead of σ− ). Producers cannot realize their price and quantity anticipations. In the

following, we assume that firms sell the entire quantity produced at the market-clearing

price ˆ tp (different from the anticipated price).10 Using (5), the realized price is determined

as:

t̂ t td x N= = ˆ tt t

Y Yp

mx mN= = (12)

Figure 2 depicts the temporary goods market equilibrium.

At this point in the paper, it might be worthwhile to trace explicitly the money circuit

corresponding to the market transactions described so far. Money is only used as a means

of transaction and its quantity, denoted by Q, is assumed to be given. On Monday morning,

the households in their quality of firms’ owners hold the entire quantity of money. At the

conclusion of the bargaining process, firms borrow part of it to pay the workers’ wages.

Taking into account the unemployment benefits, part of the quantity of money is

redistributed to the unemployed. On Friday morning, the entire quantity of money is in the

hand of the households in the form of wages, unemployment benefits and money holdings.

On Friday, the households’ consumption demand is determined under a cash in advance

constraint. Market prices are therefore determined as ˆ tt t

Q Qp

mx mN= = ; i.e. by the pure

10 In principle, producers as monopolists can also decide to sell a smaller quantity than the

produced one when entering the market. However, they do not have an incentive to do so:

On the basis of an elasticity of demand greater (anticipated demand) or equal to 1 (true

demand) in absolute terms, revenues do not increase with a quantity restriction. In addition,

at that moment, production costs are already sunk and maximizing revenues also

maximizes profits. Therefore, quantity restrictions cannot increase profits. Currie and

Kubin (2002) also explore an alternative quantity-rationing scheme.

12

quantity theory of money. Firms receive as revenue the entire quantity of money, which

they redistribute totally to households as realized profits, given by the difference between

revenues and wage payments, and as debt repayments corresponding to the wages paid in

advance.11 Therefore, total realized nominal income Y as the sum of nominal wage

payments and realized nominal profits is always equal to the quantity of money Q; the cash

in advance constraint coincides with an income constraint in the consumer maximization

problem. From now on, we take the quantity of money and thus the nominal income as

numéraire.

Finally, on Saturday firms and unions update their information. The position of firm i’s

anticipated demand function changes on account of the realized price ˆ tp and the realized

demand ˆtd . Inserting this information into equation (7) determines the position of the

anticipated demand for the period t+1:

1ˆ ˆt t tK d pσ

+ = (13)

Similarly, workers’ reservation wage adjusts in the light of the realized nominal wage tW

and of the realized employment tN .

3. The dynamic system

3.1. Outline

The dynamic behaviour of the model involves two processes. First, as suggested above, the

position of the anticipated demand function (and thus of the anticipated marginal revenue)

11 In order to keep our analysis simple, we assume no interest payments.

13

shifts over time. For a given nominal reservation wage and marginal revenue function, the

efficient bargaining outcome, ²tMR WR= , determines employment. Since all firms are

identical, equation (10) can be written as:

1t t t

me K WR

L

σσσ

−� �� �= � �� �−� �� �

(14)

where tt

mNe

L= denotes the employment rate. Taking into account equations (12) and (13),

it can also be written as

( )11 1t t t

Ye e WR

L

σ σσσ σ

σ

−−−

−� � � �= � � � �−� � � �

(15)

Second, the nominal reservation wage, tWR , is also adjusted over time.

For expository purposes, in what follows we begin our study with the dynamics of the first

process in isolation by assuming a nominal reservation wage invariant over time. After that

we specify the adjustment of the reservation wage explicitly and explore the dynamic

properties of the full system.

3.2. Goods market dynamics in isolation

If we assume a reservation wage fixed at an arbitrarily chosen level, tWR WR= , the implied

dynamic process is

( )11 1t t

Ye e WR

L

σ σσσ σ

σ

−−−

−� � � �= � � � �−� � � �

(16)

Equation (16) is a one-dimensional first-return map with the following fixed point and first

derivative

14

( )1

1

1Y

e WRL

σσ

−−� �� �= � �� �−� �� �

(17)

( ) ( ) 11

1 11

FPt

tt

e YWR e

e L

σ σσ σσ σ σ

σ

−− −

−−

∂ � � � �= − = −� � � �∂ −� � � � (18)

As long as σ > 1, the fixed point increases with σ but loses stability at σ = 2. Equation (18)

shows that the derivative of the first return map is negative for all values of the employment

rate; therefore, the time path diverges for σ > 2. Deregulating the goods market increases

stationary employment but may eventually lead to instability.

Figure 3 illustrates the period 2 cycle occurring precisely at σ = 2. The employment rate

alternates between e1 and e2; the anticipated demand and anticipated marginal revenue

functions shift accordingly. Starting with the anticipated demand function 1 and the

corresponding anticipated marginal revenue function 1 the bargaining process results in the

higher employment rate e1. The realized market price is below the anticipated one. The

anticipated demand and marginal revenue functions shift downward to the position 2. The

next bargaining results in the lower employment rate e2. The market price is now above the

anticipated one inducing an upward shift of the anticipated demand and marginal revenue

back to their respective position 1.

3.3. The nominal reservation wage as a function of the employment rate

Next, we introduce a nominal reservation wage that depends positively on the employment

rate, 1( )−=t tWR WR e : A higher employment rate is considered to increase the expected

employment probabilities outside the firm under consideration and thus to increase the

reservation wage. As a consequence, the adjustment of the nominal reservation wage

affects the goods market dynamics. The resulting dynamic system is still one-dimensional:

15

( )11 1( )

1

σ σσσ σ

σ

−−−

− −� � � �= � � � �−� � � �

t t t

Ye e WR e

L (19)

The fixed point is

( )1

1( )1

σσ

−−� �� �= � �� �−� �� �

Ye WR e

L (20)

Note that rising σ still increases the equilibrium employment rate

1 0( 1)

e e e WReWRσ σ σ

� �∂ ∂= + >� �∂ − ∂� �

The first derivative of (19) is

( ) 11

1 1 1

1 11

σ σσ σσ σ σ σ σ

σ

−− − −

−− − −

� �∂ ∂ ∂� � � �= − − = − −� �� � � �∂ − ∂ ∂� � � � � �

FPt t t t

t tt t t t

e e WR WRY eWR e

e L WR e eWR (21)

The fixed point now loses stability at some σ < 2; beyond that value the time path diverges.

Therefore, a positive influence of the employment rate on the nominal reservation wage

destabilizes the economy.

Figure 3 also illustrates this destabilizing effect. Start from the market result 1 and consider

the determination of position 2. The anticipated demand and marginal revenue functions

shift again towards their position 2; but now, in addition, the nominal reservation wage is

increased because of the high realized employment rate e1. Therefore, the new employment

rate 2 will be below e2 in Figure 3. The increase in the nominal reservation wage thus

increases the fluctuations. The process is destabilized.

3.4. The nominal reservation wage as a function of the employment rate and of its lagged

value

Finally we allow for a positive influence of the lagged reservation wage upon its current

value:

16

1 1( , )− −=t t tWR WR e WR (22)

For the moment,12 we assume the function ( )gWR to be monotonically increasing in both

arguments. The rationale for the dependence of the nominal reservation wage on the

employment rate is as sketched above; for the second one it runs along the following lines:

a high reservation wage in t-1 will result in a high bargained nominal wage rate in t-1,

which in turn is expected to raise the nominal reservation wage in t.

The dynamic system is now two-dimensional and given by equations (15) and (22).

Figure 3 can be used to illustrate that the additional effect introduced by equation (22) is

potentially stabilizing. Start again with the market position realized in period 1 and consider

the determination of the position 2. The anticipated demand and marginal revenue functions

shift to their respective position 2. Two factors change the nominal reservation wage. As in

the previous case, the high employment rate e1 tends to increase it. At the same time, the

high employment rate e1 implies that the bargained nominal wage in period 1 was

comparatively low. This would reduce the nominal reservation wage, thus introducing a

stabilizing element.

Without specifying explicitly the dynamic adjustment process for the nominal reservation

wage, it is difficult to assess the stability properties. We provide such a specification in the

following section and explore the dynamics of the full model.

4. Fully specified dynamics and numerical simulations

12 But see below the discussion in section 5.

17

We model the reservation wage as the income expected by the trade union for members

who do not find employment in the firm under consideration (see Layard et al., 1991). It

therefore depends on the expected probability of finding employment in other firms, on the

wage rate expected to be paid by other firms and on the unemployment benefit Bt.13

Consonant with the monopolistic competition set up, we assume that the trade unions do

not take into consideration reactions of other firms and the impact of their own decisions on

the aggregate variables. The expected probability of finding employment in other firms and

the expected wage rate outside the firm under consideration is therefore given by the

respective values realized in the previous period.14

1 1 1(1 )t t t t tWR e W e B− − −= + − (23)

13 We did not incorporate explicitly the financing of the unemployment benefit. However,

we studied the case of financing it out of a general labour income tax that applies both to

workers and unemployed (similar to Calmfors and Johansson, 2001): Equation (6) would

be modified to

( )1

1β β

τ−

� � � � �− −− �� � � �� � � ��

%% % %

i i ii it t t t

t t tt t

W WR p WN N

P P

where τ%t denotes the anticipated tax rate, with 1τ τ −=%t t . On Tuesday, the tax rate is adjusted

to match the benefit payments required by the realized unemployment:

( ) ( )1 1i it t t t t t t t t

i

W N W e L B e Lτ τ τ= = − −� and money holdings are redistributed

accordingly. This extension does not change the bargaining results and the following

analysis.

14 Equation (18) involves trade unions anticipating a nominal reservation wage on the basis

of naïve expectations. In the Appendix, we explore also the case of adaptive expectations.

18

The unemployment benefit is determined by applying a fixed replacement ratio φ to the

nominal wage rate earned in the lost job, Bt = φWt–1.

1 1 1 1(1 )t t t t tWR e W e Wφ− − − −= + − (24)

This formulation is more explicit than the one provided by Blanchard and Giavazzi (2003);

in contrast to their specification in real terms, it comes more natural in nominal terms.15

Using equation (9) the system (15) and (24) can be written as

11 1t t t

Ye e WR

L

σσσ σ

σ

−−−� �� � � �= � �� � � �−� � � �� �

(25)

( )1 1 1 1

1 11

1 1t t t t tWR e WR e WRσ β σ βφ

σ σ− − − −− + − +� � � �= + −� � � �− −� � � �

(26)

Appendix 1 investigates analytically the properties of the dynamic system (25)-(26).

The fixed point solutions are given by

15 Note that our instability result does not depend upon this difference in specification. With

a real reservation rate twr , the bargaining problem in equation (6) is modified to

1i i i

i it t tt t t

t t

W p Wwr N N

P P

β β−� �� � � �−−� �� � � �� � � �� �

%% %

and the results in equation (11) to 1 i

tt

t

pwr

Pσ

σ− =

%% . Blanchard and Giavazzi (2003) only

allow for a dependence of the reservation wage upon the (un-)employment rate. The central

dynamic equation therefore is

( )1 1 11

it

t t t tt

pe e e wr e

P

σ σσσ

− −

− − −� � = = � �−� �

%%

and the derivative at the fixed point is given by 1 1

1t t

t t

e e wre ewr

σ− −

∂ ∂= −∂ ∂

. Thus, also in this

case the fixed point loses stability for sufficiently high values of σ .

19

( )( )( )( )

1 11 1

eσ φ φβσ β φ

− − −=

− + −

1 YWR

eLσ

σ−= (27)

They exhibit the usual comparative static properties: goods and labour market deregulation

– as reflected in a higher value of σ and in lower values of β and φ, respectively – engender

a higher employment rate. The analysis further shows that the fixed point is stable only for

low values of σ and for high values of β and φ. However, in contrast to the one-dimensional

models studied previously, the stability loss now occurs through a Flip bifurcation giving

rise to attracting period-two cycles. Therefore, goods and labour markets deregulation –

though increasing the stationary employment rate – may destabilize the economy, but it

does not lead to diverging time paths. Appendix 1 also shows that adaptive expectations

stabilize the system but the main conclusions still carry over: stability is lost through a Flip

bifurcation; it occurs at higher degrees of deregulation and the engendered fluctuations are

less pronounced.

So far, we have explored analytically the dynamic properties of the system (25)-(26). We

now turn to a small calibration exercise. Note that the fixed point solutions only depend

upon three parameters: the parameter reflecting the degree of monopoly power in the goods

market, σ; and the two parameters related to the extent of labour market regulation, namely

the bargaining power of trade unions β and the replacement ratio φ. These parameters are

subject to the following boundaries: 1 < σ, 0 < β < 1 and,1

01

σφσ β

−< <− −

- the latter

ensuring a positive employment rate at the fixed point. Choosing an upper limit for σ

therefore allows studying the entire parameter space numerically. In our exercise, we

assumed σ ≤ 30 (implying a mark-up larger than 0.034).

We searched for numerical values of β, φ and σ such that the fixed point approximates two

macroeconomic stylized facts; namely that in 1990s Continental Europe the employment

20

rate typically assumes values above 0.8 and that the wage share typically assumes values

slightly below 0.6.16 In addition, we ask which dynamic properties the time path exhibits

close to the fixed point. Our numerical exploration shows that parameter constellations

exist which result in plausible fixed points, which are stable for highly regulated markets

and which lose stability with goods or labour market deregulation. With naïve expectations,

fluctuations are typically strong and the employment rate hits quickly its upper boundary of

one; with adaptive expectations, cyclical time paths exist with comparatively small

amplitudes, hitting no boundary condition.

5. An alternative institutional set-up

In this section, we consider a different specification for the unemployment benefit

mirroring an institutional set-up close to a social assistance scheme (see e.g. Layard et al.,

1991; and Pissarides, 1998). According to such specification, the compensation for the

unemployed is fixed in real terms (corresponding to a certain CES utility level ω ) and the

nominal payment is adjusted each period to the price index, 1t tB Pω −= . The unemployment

benefit systems in the OECD countries are found in between this alternative specification

and the one considered in the previous section where a fraction of the past period earned

wage was assigned to the unemployed (see Goerke, 2000).

The dynamic system now is

16 Taking the average over a significant group of European Countries, Giammarioli et al.

(2002) estimate that in the 1990s the labour share was 0.586 in the Business sector, 0.58 in

Industry and 0.536 in the Tradable Services.

21

11 1

σσσ σ

σ

−−−� �� � � �= � �� � � �−� � � �� �

t t t

Ye e WR

L (28)

( )1 1 11

11

1σ β ω

σ− − −−

− +� �= + −� �−� �t t t t

t

YWR e WR e

Le (29)

A crucial feature of this system is that the realized market position impacts on the dynamics

both through shifts of the demand function, implicit in equation (28), and through the

determination of the nominal reservation wage, as shown in equation (29). The analytical

structure of this specification is more complex than the one presented in the previous

section, in which the realized market position was affecting the dynamics only through

shifts of the demand function. Note that – in contrast to the assumption in the previous

sections – the partial derivative 1−

∂∂

t

t

WRe

need not be positive since with the assumed

specification a high employment rate in period t-1 not only means a high expected re-

employment probability in period t but also – via a low realized price in t-1 – a low nominal

unemployment benefit in t. The latter indirect effect of the employment rate on the nominal

reservation wage was not present in the previous sections.

The fixed point corresponding to the system (28) and (29) is given by

1 1

and1

Ye WR

eLσ σω σ

σ β σω σ− − −= =

− + − (30)

The major conclusions from the previous case carry over: As is shown in Appendix 2,

deregulation in the goods market – as reflected in a higher value of σ – or in the labour

market – as reflected in lower values of β and ω – increases the stationary employment rate,

but may eventually lead to a Flip bifurcation of the fixed point giving rise to attracting

period two cycles. Therefore, the basic trade off remains present: Deregulation increases

employment rates but may destabilize the economy. Appendix 2 also shows that adaptive

22

expectations reduce local instability as the Flip bifurcation occurs at higher degrees of

deregulation. However, this case is more complex than the previous one: Too strong

regulation may lead to instability via a Hopf bifurcation of the fixed point which gives rise

to an attracting circle. Figure 4a illustrates this point by means of a bifurcation diagram,

which plots the changes in the attractor (i.e., the resting position) of the system as the

parameter σ is varied, keeping the other parameters constant: we assume 3.63 ≤ σ ≤ 6.43,

β = 0.35, ω = 0.67; in addition, we assume naïve expectations for trade unions and adaptive

expectations for firms, with α = 0.35 representing the speeds at which firms revise their

anticipations on the position of the demand function. Below σHopf, deregulating the goods

market stabilises the system. For σHopf < σ < σFlip the system converges to the fixed point.

However, additional deregulation may destabilise the fixed point giving rise to a stable

period-two cycle, as σ passes through σFlip, or to a more complex dynamics, as σ is further

increased above σ , where the system undergoes a Hopf bifurcation of the second iterate:

the period two cycle loses stability and another stable attractor is created that consists of

two circles. Figures 4b and 4c consider specifically the latter case for 6.35σ σ= > : Figure

4b shows the two-part attractor and figure 4c plots a time path for the employment rate.

Note that it exhibits a pattern much closer to the typical features of a business cycle than the

period-two cycle after the Flip bifurcation.

23

6. Conclusion

In this paper, we have analyzed the dynamics17 of a model that follows closely the

prototype specification put forward by Blanchard and Giavazzi (2003) combining

monopolistic competition in the goods market and efficient bargaining in the labour market.

The dynamics results from two sources: First, inherent to monopolistic competition is the

assumption that even in equilibrium firms do not act upon knowing the full model. In

particular, each supplier sets prices according to a partial demand price elasticity (which is

higher than the value that takes into account all interdependencies). Assuming the same

limitations to knowledge outside equilibrium, each firm will adjust the position of the

anticipated demand function according to previous market realizations. Second, bargaining

in the labour market is based on a reservation wage reflecting the expected income outside

the firm under consideration. This anticipation is also adjusted in the light of realized

market results.

While the bargaining process may be specified in various forms, the goods market

dynamics is directly implied by the mechanism at the core of the monopolistic competition

model. It is difficult to imagine fundamentally different specifications without leaving the

assumed market structure. We showed in the paper, that the first process destabilizes the

economy: Deregulation does increase the stationary employment rate, but engenders

diverging time paths. Introducing various plausible specifications for the adjustment

process of the reservation wage dampens this sharp result: The stability loss occurs through

a Flip bifurcation giving rise not to diverging time paths but to attracting period-two cycles

17 We deliberately focused on the transition to the short run general equilibrium. As Currie

and Kubin (2002) showed the transition to a long run general equilibrium does not mitigate

the short run instability properties.

24

and eventually to complex time paths. However, the basic trade-off remains: Deregulation,

while increasing the stationary employment, may lead to instability.

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Oxford).

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Macroeconomic Model of Monopolistic Competition, Journal of Macroeconomics 23, 441-

458.

Maussner, A., 1992, Monopolistische Preisbildung und Nachfrageerwartungen in

makroökonomischen Modellen. Tübingen: Mohr.

Maussner, A., 1996, Monopolistic Price setting, subjective demand, and the business cycle.

In: Barnett, W.A., Gandolfo, G. and C. Hillinger (eds.): Dynamic disequilibrium modelling:

Theory and applications. Cambrudge: Cambridge University Press.

McDonald, I. and R. Solow, 1983, Wage Bargaining and Employment, American

Economic Review LXXIII, 896-908.

McMorrow, K. and W. Roeger, 2000, Time - Varying Nairu / Nairu Estimates for the EU’s

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26

Pissarides, C., 1998, The impact of employment tax cuts on unemployment and wages; The

role of unemployment benefits and tax structure, European Economic Review 42, 155-183.

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University Press, Cambridge).

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Comment, The American Economic Review 83, 295-301.

�������������������

��� ������������������� ������� ���

27

Appendix 1Equation Section 11

In this appendix we examine some of the properties of the dynamic system related to the

case in which the employment benefit is a proportion of the nominal wage rate earned in

the lost job, Bt = φWt–1. Assuming adaptive expectations, the dynamic system is

( ) ( )11 11t t t

L YK K e

m L

σσα α −

− −� �= − + � �� �

(A1.1)

( ) ( )1 1 1 1 1

1 11 1

1 1t t t t t tWR WR e WR e WRσ β σ βγ γ φ

σ σ− − − − −� − + − + � � � �= − + + −� � � � �− −� � � ��

(A1.2)

According to equation (A1.1) firms update their information over the position of the

demand function on the basis of the realised market position at the speed measured by the

parameter α, where 0 ≤ α ≤ 1. Similarly, equation (A1.2) clarifies that trade unions update

their expectations on the reservation wage on the basis of the bargaining outcome at the

speed measured by the parameter γ.

Using ( )1 1 11t t t

me K WR

L

σσσ

σ

−−

− − −� �= � �−� �

the system is two dimensional in tK and tWR .

For naïve expectations, i.e. for 1α γ= = , the system reduces to the system as given in (25)

and (26):

( )11t t

L YK e

m L

σσ−

−� �= � �� �

or ( )11 11t t t

Ye e WR

L

σ σσ σ

σ

−−

− −� � � �= � � � �−� � � �

(A1.3)

( )1 1 1 1

1 11

1 1t t t t tWR e WR e WRσ β σ βφ

σ σ− − − −− + − +� � � �= + −� � � �− −� � � �

(A1.4)

A1.1 Fixed point and comparative statics

From (A1.1) and(A1.2), we solve for the stationary values of the employment rate, the

position of the demand function and the reservation wage

������������������ ���� ���

28

( )( )( )( )

1 11 1

eσ φ φβσ β φ

− − −=

− + − (A1.5)

( )1L YK e

m L

σσ−� �= � �

� � (A1.6)

1 Y

WReL

σσ−= (A1.7)

0 1e< < iff ( 1)(1 ) 0σ φ φβ− − − > and 0β > (A1.8)

The stationary price is Y

peL

= and the stationary nominal wage is 1

1W WR

σ βσ− +=

−. It

follows that the stationary real wage and the stationary real reservation wage are given by:

1 1σ β σσ σ

− + −= =w wr (A1.9)

From (A1.5) to (A1.9), the stationary state solutions depend on φ, β and σ. The comparative

statics with respect to σ involves:

2 0( 1 ) (1 )

e βσ σ β φ

∂ = >∂ − + −

(A1.10)

( )

( )2 2 2

1 1 11 0 0

βσ σσ σ σ σ σ σσ

∂ ∂ ∂ − ∂� �= − − = > = >� �∂ ∂ ∂ ∂� �

WR Y e w wre

Le (A1.11)

with ( )0 ( )( 1)

WR e efor

σ σ σ σ∂ ∂≥ < ≤ >∂ ∂ −

β impacts on e , WR and w in the following way

2

10

( 1 ) (1 )e σβ σ β φ

∂ −= − <∂ − + −

(A1.12)

2

1 10 0

WR Y e wLe

σβ σ β β σ

∂ − ∂ ∂� �= − > = >� �∂ ∂ ∂� � (A1.13)

29

φ impacts on e and WR in the following way

2 0( 1 )(1 )

e βφ σ β φ

∂ = − <∂ − + −

(A1.14)

2

10

WR Y eLe

σφ σ φ

∂ − ∂� �= − >� �∂ ∂� � (A1.15)

A1.2 Bifurcation analysis

The Jacobian evaluated at the fixed point is

( )( ) ( )( )

12

1

1

1 1 1 11

1

E

eL Ym Le

Jm YeL Le

σ

σ

ασ ασ

σ φ φβ σ φ φβγ σ

σ σ

−

−

� � �− �� �� � �=

�− − − − − −� � �−� � − �� ��

(A1.16)

Its Determinant and Trace are:

( ) ( )( )1 1det 1 1

1σ φ φβ

ασ γσ ασ

− − −= − − −

−EJ (A1.17)

( )( )1 1

tr 21

σ φ φβασ γσ

σ− − −

= − −−EJ (A1.18)

with det 0EJ−∞ < < .

The violation of one of the following conditions would lead to instability for the system (in

brackets the type of bifurcation involved):

(i) ( ) ( )( )1 11 det 1 0

1σ φ φβ

ασ γω ασ

− − −− = + − >

−EJ (Hopf bifurcation);

(ii) [ ]1 tr det ( 1)(1 ) 01

σαγ σ φ φβσ

− + = − − − >−E EJ J (Saddle node bifurcation);

30

(iii) ( ) ( ) [ ]1 tr det 2 2 2 ( 1)(1 ) 01

σασ α γ σ φ φβσ

+ + = − − − − − − >−E EJ J

(Flip bifurcation).

Conditions (i) and (ii) always hold as long as condition (A1.8) holds. The Flip bifurcation is

the only possible.

We first study the case of naïve expectations in which 1α γ= = . Condition (iii) then

reduces to

( ) [ ]2 2 ( 1)(1 ) 01

σσ σ φ φβσ

− − − − − >−

(A1.19)

Note that condition (A1.8) and (A1.19) can only hold simultaneously for 1 2σ< < , which

therefore is a necessary condition for a positive and stable fixed point employment rate. If

condition (A1.19) is not satisfied, the system loses stability through a Flip bifurcation.

Figure 5, upper panel, visualizes condition (A1.8) and (A1.19), i.e. the parameter set for

which the fixed point employment is positive and stable, for 0 35.β = .

Analytically, the parameter set has to satisfy the following conditions (*Pos denotes the

parameter value for which condition (A1.8) holds with an equality sign, *Flip denotes the

parameter value for which condition (A1.19) holds with an equality sign):

( ) ( )( ) ( )2 11 11 2 1Flip Posσ σφ φβ σ β σ β

φ φσ φ− −− −= − − < < − = (A1.20)

( )( )

( )2 11 1

2 11 1 1

σ σσ σφ φ φσ β σ σ β σ β

− −− −= − < < = <− + − + − +

Flip Pos (A1.21)

( ) ( )

21 1

1 12 3 2 3 3 1

Flip Posφ φβ φ φβ φβ φβσ σ σφ φ φ φ

� �+ + + += + + + > > + =� �� �− − − −� � (A1.22)

31

Therefore, deregulating labour and goods markets (i.e reducing β or φ or increasing σ )

eventually leads to a Flip bifurcation.

For the general case of adaptive expectations, i.e. 0 1α< < and 0 1γ< < , it can be shown

that

( ) ( )det 0 1;0 1 det 1E EJ Jα γ α γ< < < < < = = (A1.23)

( )det 0 1;0 1

0EJ α γα

∂ < < < <<

∂

( )det 0 1;0 10EJ α γ

γ∂ < < < <

<∂

(A1.24)

( ) ( )tr 0 1;0 1 tr 1E EJ Jα γ α γ< < < < < = = (A1.25)

( )tr 0 1;0 1

0EJ α γα

∂ < < < <<

∂

( )tr 0 1;0 10EJ α γ

γ∂ < < < <

<∂

(A1.26)

Therefore, adaptive expectations stabilize the system.

32

Appendix 2Equation Section 12

In this appendix we study the dynamic system related to the case in which the employment

benefit is fixed in real terms and its nominal counterpart is adjusted to the realized price,

1ω −=t tB P . The dynamic system is

( ) ( )11 11t t t

L YK K e

m L

σσα α −

− −� �= − + � �� �

(A2.1)

( ) 11 1 1

1

111

1t

t t t tt

e YWR WR e WR

e Lσ βγ γ ω

σ−

− − −−

� �−− += − + +� �−� � (A2.2)

Using ( )1 1 11t t t

me K WR

L

σσσ

σ

−−

− − −� �= � �−� �

the system is two dimensional in tK and tWR . For

naïve expectations, i.e. for 1α γ= = , the system reduces to the system as given in (28) and

(29)

( )11t t

L YK e

m L

σσ−

−� �= � �� �

or ( )11 11t t t

Ye e WR

L

σ σσ σ

σ

−−

− −� � � �= � � � �−� � � �

11 1

1

111

tt t t

t

e YWR e WR

e Lσ β ω

σ−

− −−

−− += +−

(A2.3)

A2.1 Fixed point and comparative statics

Apart from the employment rate, the stationary values for all other variables correspond to

those of the previous model; also the partial derivatives with respect to σ and β are as

before. The stationary employment rate is given by

1

1e

σ ωσσ β ωσ

− −=− + −

(A2.4)

For further convenience note

33

wr

ew

ωω

−=−

(A2.5)

If wrω < and β > 0, then wr w< and 0 1e< < .

We have

( )

( ) 2

1 ( )0

we

w w

ω β σ ωβσ σ σ ω

− + −� ∂ � = >∂ −� �

(A2.6)

and

2 0( )

e wrw

ωβ σ ω

∂ −= − <∂ −

(A2.7)

The impact of changes in ω is given by

2

10

( )e

wβ

ω σ ω∂ = − <∂ −

2

10

WR Y eLe

σω σ ω

∂ − ∂� �= − >� �∂ ∂� � (A2.8)

A1.2 Bifurcation analysis

The Jacobian evaluated at the fixed point is

( ) ( )

12

1 2

1

11 1

1

σ

σ

ασ ασ

σ β σ ωγ ω γ γ σ βσ σ

−

−

� � �− �� �� � �= �− +� � � � � �− − − + − −� �� � �− �� � � � ��

E

Y LeLe m

Jem Y

eeL Le

(A2.9)

Its Determinant and Trace are:

( )2

det 1 1 11 1EJ e

σ σωασ γ γ σ β ω γασσ σ

� � �= − − − − + − + −� � �− −� �� (A2.10)

( )2

tr 2 11EJ e

σασ γ γ σ β ωσ

� = − − − − + − �−�

(A2.11)

34

The violation of one of the following conditions would involve instability for the system (in

brackets the type of bifurcation involved):

(i) ( ) ( ) ( )2

1 det 1 1 1 01EJ e

σ ωα γ σ γ γ σ β γ ασ

− = − + + − + − − >−

(Hopf bifurcation);

(ii) 1 tr det 1 1 01E EJ J

wrσω ωγασ γασ

σ� � � �− + = − = − >� � � �−� � � �

(Saddle node bifurcation);

(iii) ( )2

1 tr det 4 2 2 2 1 1 01 1E EJ J e

σ ω σωασ γ γ σ β αγσσ σ

� � �+ + = − − − − + − + − >� � �− −� ��

(Flip bifurcation).

Conditions (ii) always holds as long as and ω>wr .

In the case of naïve expectations 1α γ= = (i) and (iii) reduce to

(i) ( )1 det 1 1 0EJ eσ β− = + − + > (Hopf bifurcation);

(iii) ( )1 tr det 2 2 1 1 0E EJ J ewrωσ β σ � �+ + = − − + − − >� � ��

� � (Flip bifurcation)

In the case of naïve expectations, condition (i) always holds; the Flip bifurcation is the only

possible. Condition (iii) corresponds to

(3 2) (4 3 ) ( 1)( ) (3 4)

0( 1)( )

wr wr wr wr

wr wr wr

σ ω σ β σ ω σ σω

σ ω β

� � − + − − − − − −� � >� − − +�

(A2.12)

In this condition for stability, the denominator is always positive. Therefore, the system is

stable for

(3 2) (4 3 ) ( 1)( ) (3 4)wr wr wr wrσ ω σ β σ ω σ σω� � − + − > − − − −� �

We may distinguish three cases depending on σ.

35

Case 1: 43

σ < . The stability condition is satisfied for all other parameter values:

Case 2: 4

23

σ< < . The stability of the system depends upon the parameter values. There

are three sub-cases that we have to take into account depending on ω:

Case 2a: 3 43 2

wrσωσ

−<−

. It follows ( ) ( )3 4 3 2 2wrσ σ ω σω− > − > . In this case, the

stability condition is never satisfied.

Case 2b: 3 4 3 43 2

wr wrσ σωσ σ

− −< <−

. The system is stable for

( )( 1) (3 4)

0(3 2) (4 3 )

σ ω σ σωβ β

σ ω σ

� − − − −� > = >� − + −�

Flipwr wr

wr wr (A2.13)

If β falls below this value, the system loses stability through a Flip bifurcation.

Case 2c: 3 4 3 43 2

wr wr wrσ σ ωσ σ

− −< < <−

. The system is stable for

( )( 1) (3 4)

0(3 2) (4 3 )

σ ω σ σωβ β

σ ω σ

� − − − −� > > =� − + −�

Flipwr wr

wr wr

That is, the system is always stable.

Case 3: 2 σ< . As for Case 2, the stability of the system depends upon the parameter

values. Depending on ω we may identify two sub-cases:

Case 3a: 3 43 2

wrσωσ

−<−

. As in Case 2a, the stability condition is never satisfied.

Case 3b: 3 4 3 43 2

wr wr wrσ σωσ σ

− −< < <−

. As in Case 2b, the system is stable for

36

( )( 1) (3 4)

0(3 2) (4 3 )

σ ω σ σωβ β

σ ω σ

� − − − −� > = >� − + −�

Flipwr wr

wr wr (A2.14)

If β falls below this value, the system loses stability through a Flip bifurcation. Figure 5,

lower panel, visualizes the stability conditions for 0 35.β = .

Not much can be said for the general case 0 1α< < and 0 1γ< < . The only clear-cut

results are

( )det 0 1;0 1

0EJ α γα

∂ < < < <<

∂ and

( )tr 0 1;0 10EJ α γ

α∂ < < < <

<∂

(A2.15)

Therefore, reducing α reduces the likelihood of a Flip bifurcation; in this sense it stabilises

the system. However, in the general case, a Hopf bifurcation, which adds a destabilising

moment to the model, is not excluded.

Numerical investigations confirm these results.

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